Stochastic resonance of double fractional-order coupled oscillator with mass and damping fluctuations

In this study, the stochastic resonance phenomenon of a coupled double fractional-order harmonic oscillator with mass and damping fluctuation is investigated. Firstly, the Shapiro-Loginov formula and Laplace transform are used to obtain the analytical expression of the output amplitude gain of the system output. On this basis, aiming at the key factors involved in the model, including the coupling structure, fractional system, random fluctuation and external periodic force, the influence of coupling coefficient, double fractional order and driving frequency on the output amplitude gain (OAG) is analyzed, and reasonable physical explanations are provided. Secondly, numerical simulations are carried out to verify the accuracy of the theoretical solutions. The simulation results show that under certain conditions, the OAG of the system can appear stochastic resonance phenomenon with the above parameters, especially: (1) The OAG with the change of external drive frequency appears double peak, single peak and single valley stochastic resonance phenomenon, which does not appear under the same external disturbance with integer order and uncoupled conditions; (2) The order of double fractional derivative significantly affects the variation trend of OAG; (3) The coupling coefficient is not sensitive to the OAG.